By a result of Day we know that closed monoidal structures on presheaf categories are equivalent to promonoidal structures on the base. Building on the work of Power, I will discuss the equivalent result in the setting of premonoidal categories. Along the way we will see how a slight modification of premonoidal categories known as effectful (generalised Freyd) categories can be seen to be pseudomonoids in a bicategory of V^2-categories equipped with a version of the funny tensor product. Finally, I will discuss a generalisation of the Pastro-Street double (aka the category of coend optics) over a premonoidal category and its monoidal-like structures.